Navigation systems (such as, inertial navigation systems (INS), attitude heading reference systems (AHRS)) that use micro-electro-mechanical system (MEMS) sensors cannot gyrocompass, since MEMS sensors are low quality gyroscopes, typical greater than 2 degrees per hour bias stability for over periods, generally, greater than 10 minutes (long-term), but less than 2 degrees/hour bias for periods, generally, shorter than 10 minutes (short-term). Therefore navigation systems that include MEMS gyroscopes cannot gyro compass and display unacceptable heading drift during free inertial navigation. The inertial sensors (inertial measurement units) with performance better than 2 degrees per hour must be used in navigations system to enable gyro-compassing and prevent this unacceptable heading drift during free inertial navigation. These high performance inertial sensors are expensive and limit the application that can use low cost MEMS gyros.